Chapter 2
Particle accelerators: From basic
to applied research
Rüdiger Schmidt (CERN) – 2011 - Version E1.0
Scientific motivation for accelerators
The interest in accelerators came first from
nuclear physics
Ernest Rutherford 1928:
I have long hoped for a source of positive particles
more energetic than those emitted from natural
radiaoactive substances
Particles from radioactive decays have energies of up
to a few MeV. The interest was to generate such
particles, e.g. to split the atomic nuclei, which was for
the first time done in 1932 with a Cockroft-Walton
Generator.
Cockcroft, Rutherford and
Walton soon after splitting
the atom
http://www.phy.cam.ac.uk/alumni/alumn
ifiles/Cavendish_History_Alumni.ppt
2
Dimensions in our universe
Typical dimension of atomic and subatomic matter:
•
•
•
•
•
•
•
Distance of atoms in matter:
Atomic radius:
Proton / Neutron radius:
Classical electronenradius:
Quark:
Range of strong interaction :
Range of Weak interaction :
•
•
Mass of an electron:
Mass of a proton :
0.3 nm = 3•10-10 m
0.1 nm = 1•10-10 m
1•10-15 m
2.83•10-15 m
1•10-16 m
< 1•10-15 m
<<1•10-16 m
9.11•10-31 kg
1.673•10-27 kg
3
Particle energy and basic research
For studies of the structure of the material, “probes“ are required which are
smaller than the structure to be examined, for example: Light microscope ( Quants with an energy of about 0.25 eV)
•
•
•
•
Electron microscopes
Particle accelerators – the probe is the particle
Particle accelerators – the probe is the radiation emitted by the particles (light
quantum with an energy of some eV up to few MeV)
Particle accelerators - the probe is a neutron. Neutrons are in general generated
with intense high energy proton beams on a target
The production of new particles requires particles with enough energy
Examples:
Particle accelerators
Cosmic rays
4
Particle energy and basic research
Extension of the probe to study material structures
Light, typical wavelength: 500 nm = 5•10-7 m
For particles, the De Broglie wavelength becomes smaller with increasing
kinetic energy:
B 
h planck
p
B 
h planck  c
2
E k  (E k  2  m 0  c )
5
Research on small structures requires high energy
Example for the De Broglie wavelength:
Kinetic energy of a proton:
𝐸𝑘𝑝 = 7000 𝐺𝑒𝑉
De Broglie wavelength for the proton:
𝜆𝐵 = ℎ𝑝𝑙𝑎𝑛𝑐𝑘 ∗
𝑐
𝐸𝑘𝑝 ∗(𝐸𝑘𝑝 +𝑚𝑝 ∗𝑐 2 )
𝜆𝐵 = 1.771 ∗ 10−19 𝑚
Kinetic energy of an electron:
𝐸𝑘𝑒 = 100 𝐺𝑒𝑉
De Broglie wavelength for the proton:
𝜆𝐵 = ℎ𝑝𝑙𝑎𝑛𝑐𝑘 ∗
𝑐
𝐸𝑘𝑒 ∗(𝐸𝑘𝑒 +𝑚𝑝 ∗𝑐 2 )
𝜆𝐵 = 1.24 ∗ 10−17 𝑚
6
PROTONS
Kinetische
Energie
b=v/c
 = E / E0
[GeV]
1
10
100
1000
10000
0.875
0.996
~1
~1
~1
2.066
11.65
107.6
1067
10660
pc
[GeV]
1.696
10.89
100.93
1000
10000
 Broglie * 1018
[m]
732.00
113.80
12.29
1.23
0.12
ELECTRONS
Kinetische
Energie
[GeV]
0.1
1
10
100
1000
b=v/c
 = E / E0
~1
~1
~1
~1
~1
196.7
1958
19570
195700
1957000
pc
[GeV]
0.101
1.001
10.01
100.001
1000
 Broglie * 1018
[m]
12340
1239
124
12.4
1.24
Energy spectrum: Cosmic radiation and accelerators
Cosmic radiation is free
of charge!
Investment for particle
physics with
accelerators:
~GEuro
LHC am CERN
But:
Cosmic rays at 1 TeV:
<0.001 particles / m2 / sec
LHC 7 TeV:
>1026 protons / m2 / sec
8
Creation of secondary particles in fixed target experiments
An accelerator that directs particles on a target:
Particles from the accelerator with the
kinetic energy E and
mass m0
Conservation of momentum and
energy
Particles in the
target with mass m1
Secondary particles from the collision
with momentum p and mass m
Fixed Target Experiment
Example: kinetic energy of a proton with
m p  1.673  10
 27
kg
E k  450 GeV with the rest mass:
:


Ek

E cm  2  m p  c 
1 
 1
2


2 mp c


2
E cm  27.244  GeV
9
Production of secondary beams
Sekundary beam:
Magnet
Target
•
•
•
•
•
•
Positrons
Antiprotons
Neutrinos
Myons
Pions
Kaons
Primary beam
Parameters: Beam Intensity and Particle type
10
Production of “new” particles with colliding beams
Accelerator where two particles collide:
Particles from the accelerator with the
kinetic energy E and
mass m0
New particle with momentum = 0
and mass m0
Conservation of momentum and energy:
Collider
Colliding particles with
E cm  2  E k
E cm  900  GeV
E k  450  GeV
Note: to produce a Z0 needs e+ e- beams
with each about 46 GeV. For the production
of W+ W-pair, the accelerator requires the
double energy (conservation of charge!)
11
Particle physics: cross section
Approximation (example): to investigate the inside of a proton, a
high-energy proton beam collides with another proton
„Protonradius“:
„Area“ is in the order of:
~10-15 m
~10-30 m2
Definition: Barn  10-24 cm2 = 10-28 m2
Diameter of the beam:
10-3 m (1 mm)
Number of protons in the beam:
1014
Probability, that a proton in the beam collides with another proton:
10-30 m2 / 10-6 m2
In order to obtain a collision rate of 1 Hz, about 1024 colliding
protons per second are required
•
•
Small cross section of the beams
Intense particle beams
12
Colliding Beams: Energy and Luminosity
N
Number of "new particles"“:
LEP (e+e-)
:
Tevatron (p-pbar) :
B-Factories
:
LHC nominal :
LHC today:
t
 L [ cm
2
 s ]   [ cm ]
1
2
3-4 1031 [cm-2s-1]
3 1032 [cm-2s-1]
>1034 [cm-2s-1]
1034 [cm-2s-1]
3-4 1033 [cm-2s-1]
e+e- storage rings: LEP-CERN until 2001, B-Factories at SLAC and KEK (USA, JAPAN)
e+e- linear accelerators (Linacs): - being discussed – ILC (Int. Linear Collider) und CLIC – CERN
Proton-Proton: ISR until 1985, und LHC – CERN from 2008
Proton-Antiproton Collider: SPS – CERN until 1990, TEVATRON – FERMILAB (USA) just finished
e+ or e- / Proton: HERA (DESY) – until 2007
13
Luminosity
L = N2 f n b / 4p  x  y
N .........
Number of particle per bunch
f .........
nb.........
 x  y ...
Revolution frequency
Number of bunches
Transverse beam dimensions at collision point (Gaussian)
Protons N per bunch: 1011
f = 11246 Hz, Number of bunches: nb = 2808
Beam size σ = 16 m
L = 1034 [cm-2s-1]
Example for LHC
14
Z0 Teilchen
bei LEP
Energy and power of a particle beam
The energy that is stored in a particle beam is given by:
𝐸𝑏𝑒𝑎𝑚 = 𝐸𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 × 𝑁𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑠
The power in the beam is given by:
𝑃𝑏𝑒𝑎𝑚
1
= 𝐸𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 × 𝑁𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑠 ×
𝑠𝑒𝑐
For many new projects high power of the beam is of crucial
importance (power exceeding one MW).
17
Energy stored in the beam
10000.00
LHC
energy in
magnets
Energy stored in the beam [MJ]
1000.00
LHC top
energy
LHC injection
(12 SPS batches)
100.00
Factor
~200
SPS fixed
target and CNGS
10.00
ISR
HERA
SPS batch to LHC
TEVATRON
1.00
0.10
LEP2
RHIC
proton
SPS
ppbar
0.01
1
10
100
1000
10000
Momentum [GeV/c]
18
Importance of particle physics for the development of
accelerators
• The driving force behind the development of accelerators came
from particle physics
• Particle physicists are still the most demanding user of particle
accelerators
• This is starting to change – now progress in accelerator physics
is being also driven by other users
19
The use of Accelerators (R.Aleksan)
Projects
Science field
Beam type
Estimated cost
LHC
Particle Physics
proton
3700M€
FAIR
Nuclear Physics
Proton /ion
1200M€
XFEL
Multi fields
electron aphoton
1050M€
ESS
Multi fields
Proton aneutron
1300M$
IFMIF
Fusion
Deuteron
aneutron
1000M€
MYRRHA
Transmutation
Proton aneutron
700M€
In past 50 years, about 1/3 of Physics Nobel Prizes are rewarding work
based on or carried out with accelerators
This « market » represents ~15 000 M€ for the next 15 years, i.e. ~1000M€/year
20
Industrial accelerators
Clinical accelerators
 radiotherapy
 electron therapy
 hadron (proton/ion)therapy
 ion implanters
 electron cutting & welding
 electron beam and X-ray irradiators
 radioisotope production
…
Total systems
(2007) approx.
System
sold/yr
Sales/yr
($M)
System
price ($M)
Cancer Therapy
9100
500
1800
2.0 - 5.0
Ion Implantation
9500
500
1400
1.5 - 2.5
Electron cutting and welding
4500
100
150
0.5 - 2.5
Electron beam and X-ray irradiators
2000
75
130
0.2 - 8.0
Radioisotope production (incl. PET)
550
50
70
1.0 - 30
Non-destructive testing (incl. security)
650
100
70
0.3 - 2.0
Ion beam analysis (incl. AMS)
200
25
30
0.4 - 1.5
Neutron generators (incl. sealed tubes)
1000
50
30
0.1 - 3.0
27500
1400
3680
Application
Total
Total accelerators sales increasing more than 10% per year
Courtesy: R. Aleksan
and R. Hamm 21